NEED FOR BIASING A TRANSISTOR:

• For a Bipolar Junction Transistor commonly called as the BJT Transistor the stability factor is defined as the change in the collector current of a Bipolar Junction Transistor (BJT) with respect to change in various transistor parameters like as Collector Leakage Current.
• The Stability factor for a BJT Transistor is denoted by S.
• The process of making operating point independent of temperature changes or variation in transistor parameters is known as stabilization.Ic is thecollector current and Icl is the collector leakage current.
• Under normal operating condition, the base-emitter junction is forward biased and the collector-base junction is reverse biased. The biasingarrangement is required to establish a stable Q-point which indicates the desired mode of operation.

FIXED BIAS:

• This form of biasing is also called base bias. The single power source is used for both collector and base of transistor, although separate batteries can also be used.
• Using KVL we have:

$V_{CC} -V_{BE} = 0 ; IB = \dfrac{(V_{CC}-V_{BE})}{R_{B}}$

  $V_{C} = \beta I_{B}= \dfrac {\beta(V_{CC}-V_{BE})}{R_{B}}$

• Using KVL in the collector-emitter loop

$V_{CC} -\beta V_{CE} = 0; V_{CE} = V_{CC} - I_{C}R_{C}$

ADVNTAGES AND DISADVANTAGES OF FIXED BIAS :

ADVANTAGE:

• Operating point can be shifted easily anywhere in the active region by merely changing the base resistor (RB).
• A very small number of components are required.

DISADVANTAGE:

• Poor stabilization
• High stability factor(S=β+1 because IB is constant so dIB/dIC =0 ), hence prone to thermal runaway

APPLICATION OF FIXED BIAS

• Due to the above inherent drawbacks, fixed bias is rarely used in linear circuits (i.e., those circuits which use the transistor as a current source). Instead, it is often used in circuits where transistor is used as a switch.

COLLECTOR BIAS VOLTAGE:

• This configuration employs negative feedback to prevent thermal runaway and stabilize the operating point.
• In this form of biasing, the base resistor RB is connected to the collector instead of connecting it to the DC source Vcc.
• So any thermal runaway will induce a voltage drop across the RC resistor that will throttle the transistor's base current.

Applying KVL

$V_{CC} = (I_{C}+I_{B})R_{C} + V_{CE}$

$ V_{CE} = I_{B}R_{B} + V_{BE} $

Since, IC = βIB s

 $I_{B}=\dfrac{V_{CC}-V_{BE}}{R_{B}+ (1 + \beta)R_{C}}$

ADVANTAGES AND DISADVANTAGES OF COLLECTOR BIAS

ADVANTAGES:

• Better stabilization compared to fixed bias

DISADVANTAGES

• This circuit provides negative feedback which reduces the gain of the amplifier

APPLICATION:

• The feedback also decreases the input impedance of the amplifier as seen from the base, which can be advantageous.
• Due to the gain reduction from feedback, this biasing form is used only when the trade-off for stability is warranted.

VOLTAGE DIVIDER BIAS:

• This is the most widely used method to provide biasing and stabilization to a transistor.
• In this form of biasing, R1 and R2 divide the supply voltage VCC and voltage across R2 provide fixed bias voltage VB at the transistor base.
• Also a resistance RE is included in series with the emitter that provides the stabilization.

$V_{B}=V_{Th}=V_{CC}=\dfrac{R2}{R1+R2}$

$R_{th}=\dfrac{R1R2}{R1+R2}$

Base Emitter Loop

 $V_{Th}-I_BR_{th}-V-{BE}-(\beta +1)I_{B}R_{E}=0$

Collector Emitter Loop

 $I_{C}=\beta I_{B}=\dfrac{\beta(V_{Th}-V_{BE})}{R_{th}+(\beta+1)R_{E}}$

For Bias stability 

$I_{C}=\dfrac{V_{Th}-V_{BE}}{R_{E}}$

The stability factor

 $S=\dfrac{(\beta+1)}{1-\beta \dfrac{dI_{B}}{dI_{C}}}$

Differentiating with respect to IC

 $V_{Th} = I_{B} R_{th}-V_{BE} -\beta (I_{B} +I_{C} )R_{E}$

  $\dfrac{dI_{B}}{dI_{C}}=\dfrac{-R_{E}}{R_{th}+R_{E}}$

 $S=\dfrac{\beta+1( R_{th}+R_{E})} {(R_{E}(1+\beta)+R_{th})}$

• For stability, S should be small which can be achieved by making RTh/R E small. For very small RTh/RE ; S = 1 (ideal case)
• For very small RTh/RE : R 2 RTh current drawan by R 2 will be large. R E Large Vcc required. Hence comproise is made in selection.
• The Stability of Voltage divider is better compared to the other two

ADVANTAGES AND DISADVANTAGES:

ADVANTAGES:

• Stability is more stable here as it is able to reach its maximum value

DISADVANTAGES:

• Circuit us a bit complex.
• Stability depends on β which is dependent upon the manufuacturer